Battery health isn’t the only indication of a batteries performance. The battery can be heavily degraded and still show a high percentage depending on many factors.
Ex: not all batteries are equal - the factory spec might be 2000 but you get lucky and get a 2300 battery - that means percentage will stay at 100% for a lot longer even though the battery is degraded.
Do you know roughly how many cycles the battery has? Unfortunately any random shutdown will cause performance management even a software or other hardware shutdown.
Go to settings - privacy - analytics and check for any logs with “panic” in the title as this is a good indication of there being a hardware issue causing restarts (note: not always - panics can be software issues but 90% of the time not the case)
If you assume cycle count under ~350 and no panic logs then restore the phone and setup as new to rule out firmware issues.